On the Ruelle-Mayer Transfer Operators for Hölder Continuous Functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911256301010944 |
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| author | Baumgartner, Alexander |
| author_facet | Baumgartner, Alexander |
| contents | We consider a family of operators connected with the geodesic flow on the modular surface. We show certain spectral information is retained after expanding their domain to the space of $α$-Hölder continuous functions on the unit interval. For example, the point spectra associated with the Maass cusp forms and non-trivial zeroes of the Riemann zeta function to the right of the critical line remain unchanged when the Hölder constant is $(1/2+\varepsilon)$ and $3/4$ respectively. We briefly consider a three-term functional equation introduced by Lewis in the Hölder setting and provide a partial classification of solutions in this setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Ruelle-Mayer Transfer Operators for Hölder Continuous Functions Baumgartner, Alexander Number Theory Dynamical Systems 37C30 (Primary) 37D35, 11J70 (Secondary) We consider a family of operators connected with the geodesic flow on the modular surface. We show certain spectral information is retained after expanding their domain to the space of $α$-Hölder continuous functions on the unit interval. For example, the point spectra associated with the Maass cusp forms and non-trivial zeroes of the Riemann zeta function to the right of the critical line remain unchanged when the Hölder constant is $(1/2+\varepsilon)$ and $3/4$ respectively. We briefly consider a three-term functional equation introduced by Lewis in the Hölder setting and provide a partial classification of solutions in this setting. |
| title | On the Ruelle-Mayer Transfer Operators for Hölder Continuous Functions |
| topic | Number Theory Dynamical Systems 37C30 (Primary) 37D35, 11J70 (Secondary) |
| url | https://arxiv.org/abs/2511.06513 |